No

Why? Because you should be inside at home! #StayHome

But if you absolutely had to go out to get groceries, medication or other essential travel, No, you don't need a jacket.

Based on the weather in (Archway), England, United Kingdom as of June 2, 2020 11:24am local time.

Now

Overcast
Temp: 70°F21°C
Wind: 6 MPH10 KPH
Precipitation: None

Today

Next 2 hours: No

Next 4 hours: No

Next 8 hours: No

Tomorrow

Yes

Overcast throughout the day.
Low of 55°F13°C, High of 65°F19°C
Wind: 7 MPH11 KPH
Precipitation: 25% rain